Question: Vanessa is 24 years older than William. Eighteen years ago, Vanessa was 4 times as old as William. How old is William now?
Solution: We can use the given information to write down two equations that describe the ages of Vanessa and William. Let Vanessa's current age be $v$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $v = w + 24$ Eighteen years ago, Vanessa was $v - 18$ years old, and William was $w - 18$ years old. The information in the second sentence can be expressed in the following equation: $v - 18 = 4(w - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = w + 24$ . Substituting this into our second equation, we get the equation: $(w + 24)$ $-$ $18 = 4(w - 18)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w + 6 = 4 w - 72$ Solving for $w$ , we get: $3 w = 78$ $w = 26$.